Problem: A puppy gains weight, $w$, at a rate approximately inversely proportional to its age, $t$, in months. Which equation describes this relationship? Choose 1 answer: Choose 1 answer: (Choice A, Incorrect) Incorrect $\dfrac{dw}{dt}=kw$ (Choice B, Incorrect) Incorrect $\dfrac{dw}{dt}=\dfrac{k}{w}$ (Choice C, Incorrect) Incorrect $\dfrac{dw}{dt}=kt$ (Choice D, Checked, Correct) Correct (selected) $\dfrac{dw}{dt}=\dfrac{k}{t}$
Answer: The weight of the puppy is denoted by $w$. The rate of change of the puppy's weight is represented by $w'(t)$, or $\dfrac{dw}{dt}$. Saying that the rate of change is inversely proportional to something means it's equal to some constant $k$ divided by that thing. That thing, in our case, is the puppy's age, $t$, in months. In conclusion, the equation that describes this relationship is $\dfrac{dw}{dt}=\dfrac{k}{t}$.